Practice Maths

L36 — Expressing One Quantity as a Fraction or Percentage of Another

Key Terms

expressing as a fraction
Writing one quantity as a part of another: part ÷ whole. E.g. 12 out of 20 = 1220 = 35.
expressing as a percentage
Converting a fraction to a percentage by multiplying by 100. E.g. 35 × 100 = 60%.
unit conversion
Changing measurements to the same unit before comparing. E.g. 500 mL out of 2 L must become 500 out of 2000 before writing as a fraction.

The Method

  1. Make sure both quantities are in the same units.
  2. Write as a fraction: part ÷ whole.
  3. Simplify the fraction.
  4. To convert to a percentage: multiply by 100.
Same units first! You cannot compare 30 minutes to 2 hours without converting. 30 minutes out of 2 hours = 30 out of 120 = 14 = 25%.

Worked Examples

Express 15 out of 25 as a fraction and percentage:

1525 = 35  →  35 × 100 = 60%

Express 250 g as a fraction of 1 kg:

Convert: 1 kg = 1000 g → 2501000 = 14 = 25%

Express 45 minutes as a percentage of 1 hour:

1 hour = 60 min → 4560 = 34 = 75%

Expressing “A as a Part of B”

This lesson is about comparison — expressing one quantity as a fraction or percentage of another. It’s behind test scores (you got 1720 — what percentage?), shopping (you saved $15 from $80 — what percentage off?), and sports statistics (8 goals from 12 shots — what fraction?). It’s everywhere.

The core method is always: write the part over the whole, simplify if needed, then multiply by 100 for the percentage.

The Critical Step: Same Units First

Before you can write a fraction, both quantities must be in the same unit. You cannot write “30 cm out of 2 m” as 302 — that’s meaningless! You must convert first: either 30 out of 200 cm, or 0.3 out of 2 m. Both give 320 = 15%.

Common unit pairs to watch:

  • Minutes and hours: 1 hour = 60 minutes
  • Grams and kilograms: 1 kg = 1000 g
  • Millilitres and litres: 1 L = 1000 mL
  • Centimetres and metres: 1 m = 100 cm
  • Cents and dollars: $1 = 100 cents
Same units first — always. This is the number-one source of errors in this type of problem.

Identifying the “Whole”

In word problems, the challenge is finding the denominator. Ask yourself: “out of what total?”

  • “12 boys in a class of 30” → whole is 30 (the total class)
  • “saved $15 from $60 weekly pay” → whole is $60
  • “8 red out of 8 red + 5 blue + 7 green lollies” → whole is 20 (total lollies)

Comparing Results: Use Percentages

When comparing fractions from different totals, convert both to percentages. Maya scored 2835 = 80%. Alex scored 3645 = 80%. Equal! Without converting, it’s hard to see.

Common mistake: In a class with 12 boys and 18 girls, the fraction of boys is 1230 (not 1218). The denominator must be the TOTAL number of students.

  1. Express as a Fraction (Same Units)

    Write each as a simplified fraction:

    1. 6 out of 10
    2. 15 out of 20
    3. 8 out of 32
    4. 12 out of 18
    5. 35 out of 100
    6. 9 out of 27
    7. 14 out of 21
    8. 20 out of 50

  2. Express as a Percentage

    Write each as a percentage:

    1. 12 out of 20
    2. 7 out of 25
    3. 18 out of 50
    4. 3 out of 8
    5. 11 out of 40
    6. 27 out of 60
    7. 5 out of 16
    8. 19 out of 200

  3. Unit Conversions First

    Convert to the same units, then express as a fraction and percentage:

    1. 30 cm out of 1 m
    2. 500 mL out of 2 L
    3. 45 minutes out of 3 hours
    4. 250 g out of 1 kg
    5. 20 cents out of $5
    6. 15 mm out of 6 cm
    7. 3 months out of 2 years
    8. 400 m out of 2 km

  4. Identify the “Whole”

    1. A class has 12 boys and 18 girls. What fraction of the class are boys?
    2. Out of 40 questions on a test, Sam got 34 correct. What percentage did Sam get right?
    3. A bag has 8 red, 5 blue, and 7 green marbles. What fraction are blue?
    4. Tom saves $15 from his $60 weekly earnings. What percentage does he save?

  5. Test Scores and Results

    1. Maya scored 28 out of 35 in Maths and 36 out of 45 in Science. Express each as a percentage. Which was the better result?
    2. A basketball team won 14 games out of 20 played. What percentage of games did they win?
    3. In a survey of 80 students, 52 preferred sport over reading. Express this as both a fraction and a percentage.
    4. A school garden covers 350 m² of the 1400 m² school grounds. What percentage does the garden cover?

  6. Comparing Amounts

    1. Bottle A holds 600 mL and is 34 full. Bottle B holds 800 mL and is 60% full. Which bottle contains more liquid?
    2. Jess read 90 pages of a 150-page book. Ben read 64 pages of a 80-page book. Who has read a greater fraction of their book?
    3. A recipe uses 120 g of sugar out of 400 g of total ingredients. Another uses 80 g out of 250 g. Express each as a percentage and identify which has the higher sugar proportion.
    4. In a lolly bag, 9 out of 36 lollies are red. Write this as a fraction, decimal, and percentage.

  7. Find the Missing Quantity

    1. If 40% of a number is 32, what is the number?
    2. If 35 of a class is 18 students, how many students are in the class?
    3. A student scored 75% on a test. If they got 45 marks, how many marks was the test out of?
    4. 25% of a recipe is flour. If 150 g of flour is used, how much total mixture is there?

  8. Express as Both Fraction and Percentage

    Express each as a simplified fraction and as a percentage:

    1. 24 out of 60
    2. 18 out of 45
    3. 30 out of 75
    4. 36 out of 90
    5. 45 out of 180
    6. 28 out of 70
    7. 55 out of 220
    8. 120 out of 400

  9. Interpreting Data from a Table

    A school canteen recorded the following orders one day:

    ItemOrders
    Pie30
    Sandwich45
    Salad15
    Fruit Cup10
    1. What fraction of orders were pies? Simplify your answer.
    2. What percentage of orders were sandwiches?
    3. What fraction of orders were either salad or fruit cup?
    4. What percentage of orders were NOT pies?

  10. Fraction, Decimal and Percentage Connections

    1. A swimming pool is 25 m long. A swimmer has completed 18 m of a lap. Express the completed distance as a fraction, decimal and percentage of the full lap.
    2. Of 120 survey respondents, 84 said they exercise regularly. Express this as a fraction, decimal, and percentage.
    3. A fundraiser has a goal of $500. So far $375 has been raised. What fraction and percentage of the goal has been reached? How much more is needed?
    4. Two classes had tests. Class A: 21 out of 28 students passed. Class B: 30 out of 40 students passed. Express each as a percentage. Which class performed better?
See Answers ➔